Zeolite beta, which is the only high-silica zeolite with a three dimensional pore system containing large 12-membered ring apertures, is a molecular sieve known to have useful catalytic properties. Synthetic methods for preparing such materials in most instances yield zeolite beta containing both silica and alumina in the lattice framework of the zeolite. In U.S. Pat. No. 3,308,069 (Wadlinger et al.), for example, zeolite betas having silica:alumina molar ratios of from 5 to 200 are described. One group of workers observed in 1988 that "[i]t is very difficult to effectively synthesize siliceous crystals of zeolite beta" [Perez-Pariente et al., Zeolites, 8, 46-53 (1988)]. More recently, procedures for obtaining all-silica zeolite beta have been disclosed. An essentially silicic beta zeolite having a silica/alumina ratio of greater than or equal to about 800 and a crystallinity of greater than or equal to about 80% was claimed in U.S. Pat. No. 5,310,534 (Fajula et al.) to have been prepared by a dealuminization procedure comprising acid leaching of a raw zeolite containing a structuring agent. Dealuminization can, however, under certain conditions result in the loss of zeolite crystallinity and the creation of framework vacancies or defects; such changes may not always be desirable, depending upon the application contemplated for the zeolite beta product. An all-silica zeolite beta has also been synthesized under hydrothermal conditions using dibenzyldimethylammonium cation as a templating agent [van der Waal, J. Chem. Soc., Chem. Commum. 1241-1242 (1994)]. In our hands, however, this method gives unsatisfactorily low yields of silicic zeolite beta (possibly due to the thermal instability of the particular templating agent used). It would be highly desirable to develop more efficient methods for preparing essentially silicic zeolite beta having a high degree of crystallinity.